Calculate all real numbers $r $ with the following properties: If real numbers $a, b, c$ satisfy the inequality$ | ax^2 + bx + c | \le 1$ for each $x \in [ - 1, 1]$, then they also satisfy the inequality $| cx^2 + bx + a | \le r$ for each $ x \in [- 1, 1]$.
Problem
Source: Czech-Polish-Slovak Junior Match 2018, Team p3 CPSJ
Tags: trinomial, algebra, inequalities